The finite sample breakdown point of l1-regression

Through a new parametric) linear programming approach, we derive a formula for the finite sample breakdown point of l(1)-regression with a given design matrix X and contamination restricted to the dependent variable. This is done using the notion of the q-strength and the s-stability of a design matrix X, which are introduced here. We discuss the relationship between our result and existing results in the literature. Finally, we demonstrate the usefulness of our result by calculating ( via the solution of mixed-integer programs) the finite sample breakdown point of l(1)-regression with contamination restricted to the dependent variable for nine well-known data sets from the robust regression literature.